Renormalization of the Cabibbo-Kobayashi-Maskawa Matrix at One-Loop Level

Abstract

We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix at one-loop level. We emphasize at one prescription which is formulated with reference to the case of no mixing of quark's generations and point out that it doesn't make the physical amplitude involving quark mixing ultraviolet finite. We then propose a revised prescription to solve this problem and simultaneously keep the unitarity of the CKM matrix. Through explicit calculations we also prove that in order to keep the CKM matrix gauge independent the unitarity of the CKM matrix must be preserved.